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Youll find explanations of mathematical skills and plenty of opportunities for practice, investigation and mental maths throughout. The accompanying .Youll find explanations of mathematical skills and plenty of opportunities for practice, investigation and mental maths throughout. The accompanying .
Cambridge Primary Mathematics Whether they are rounding decimal numbers or calculating time intervals on a train timetable, Cambridge Primary Mathematics helps your learners develop their mathematical thinking skills They’ll be fully supported with worked examples and plenty of practice exercises, while projects throughout the book provide opportunities for deeper investigation of mathematical concepts – including predicting patterns using matchsticks With key word boxes, clear diagrams and supporting illustrations, the course makes maths accessible for second language learners ãỵ Get learners thinking about what they already know with ‘Getting Started’ boxes ãỵ Help your learners think and work mathematically with clearly identified activities throughout each unit ãỵ Think like a mathematician provides learners with investigation activities ãỵ Look what I can do!’ statements in each section and ‘Check your progress’ exercise at the end of each unit help your learners reflect on what they have learnt ãỵ Answers for all activities can be found in the accompanying teacher’s resource CAMBRIDGE Primary Mathematics Learner’s Book For more information on how to access and use your digital resource, please see inside front cover This resource is endorsed by Cambridge Assessment International Education support as part of a set of Provides ỵ resources for the Cambridge Primary Maths curriculum framework (0096) from 2020 ỵHas ỵ passed Cambridge Internationals rigorous quality-assurance process ✓ Developed by subject experts ✓ For Cambridge schools worldwide Emma Low & Mary Wood Completely Cambridge Cambridge University Press works with Cambridge Assessment International Education and experienced authors to produce high-quality endorsed textbooks and digital resources that support Cambridge teachers and encourage Cambridge learners worldwide To find out more visit cambridge.org/ cambridge-international Registered Cambridge International Schools benefit from high-quality programmes, assessments and a wide range of support so that teachers can effectively deliver Cambridge Primary Visit www.cambridgeinternational.org/primary to find out more Second edition Digital access CAMBRIDGE Primary Mathematics Learner’s Book Mary Wood & Emma Low University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 79 Anson Road, #06–04/06, Singapore 079906 Cambridge University Press is part of the University of Cambridge It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence www.cambridge.org Information on this title: www.cambridge.org/9781108760034 © Cambridge University Press 2021 This publication is in copyright Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published 2014 Second edition 2021 20 19 18 17 16 15 14 13 12 11 10 Printed in Dubai by Oriental Press A catalogue record for this publication is available from the British Library ISBN 978-1-108-76003-4 Paperback with Digital Access (1 Year) ISBN 978-1-108-96418-0 Digital Learner's Book (1 Year) ISBN 978-1-108-96419-7 Learner's Book eBook Additional resources for this publication at www.cambridge.org/9781108760034 Projects and their accompanying teacher guidance have been written by the NRICH Team NRICH is an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge, which focuses on problem solving and on creating opportunities for students to learn mathematics through exploration and discussion: nrich.maths.org Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Information regarding prices, travel timetables, and other factual information given in this work is correct at the time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter NOTICE TO TEACHERS IN THE UK It is illegal to reproduce any part of this work in material form (including photocopying and electronic storage) except under the following circumstances: (i)ỵ where you are abiding by a licence granted to your school or institution by the Copyright Licensing Agency; (ii)ỵ where no such licence exists, or where you wish to exceed the terms of a licence, and you have gained the written permission of Cambridge University Press; (iii)ỵ where you are allowed to reproduce without permission under the provisions of Chapter of the Copyright, Designs and Patents Act 1988, which covers, for example, the reproduction of short passages within certain types of educational anthology and reproduction for the purposes of setting examination questions Introduction Introduction Welcome to Stage of Cambridge Primary Mathematics We hope this book will show you how interesting Mathematics can be and make you want to explore and investigate mathematical ideas Mathematics is everywhere Developing our skills in mathematics makes us better problem-solvers through understanding how to reason, analyse and reflect We use mathematics to understand money and complete practical tasks like cooking and decorating It helps us to make good decisions in everyday life In this book you will work like a mathematician to find the answers to questions like these: • What is a prime number and how you know if a number is prime? • How can you quickly find out if 642824 is divisible by 8? • If three-quarters of a number is 24, what is the number? • What time is it in Mumbai when it is a.m in Mexico City? • What is a reflex angle? • How you draw a waffle diagram? • How can a shape be translated? Talk about the mathematics as you explore and learn This helps you to reflect on what you did and refine the mathematical ideas to develop a more effective approach or solution You will be able to practise new skills, check how you are doing and also challenge yourself to find out more You will be able to make connections between what seem to be different areas of mathematics We hope you enjoy thinking and working like a mathematician Mary Wood and Emma Low Contents Contents Pages Unit How to use this book Thinking and Working Mathematically 10 1ỵ 20 Project 1: Decimal dice 21 2ỵ 2D shape and pattern 2.1ỵ Triangles 2.2ỵ Symmetry Geometry and measure 35 3ỵ Numbers and sequences 3.1ỵ Counting and sequences 3.2ỵ Square and triangular numbers 3.3ỵ Prime and composite numbers Number 47 Project 2: Pattern prediction 49 4ỵ Averages 4.1ỵ Mode and median Statistics and probability 57 5ỵ Addition and subtraction 5.1ỵ Addition and subtraction including decimal numbers 5.2ỵ Addition and subtraction of positive and negative numbers Number 67 6ỵ 3D shapes 6.1ỵ Nets of cubes and drawing 3D shapes Geometry and measure 74 7ỵ Fractions, decimals and percentages 7.1ỵ Understanding fractions 7.2ỵ Percentages, decimals and fractions 7.3ỵ Equivalence and comparison Number 87 Project 3: Puzzling percentages 88 8ỵ Probability 8.1ỵ Likelihood 8.2ỵ Experiments and simulations The number system 1.1ỵ Understanding place value 1.2ỵ Rounding decimal numbers Strand Number Statistics and probability Contentsỵỵ Pages Unit Strand 101 9ỵ Number 108 10ỵ Angles 10.1ỵ Angles Geometry and measure 116 11ỵ Multiplication and division 11.1ỵ Multiplication 11.2ỵ Division 11.3ỵ Tests of divisibility Number 129 12ỵ Data 12.1ỵ Representing and interpreting data 12.2ỵ Frequency diagrams and line graphs Statistics and probability 145 Project 4: Depicting data 147 13ỵ Ratio and proportion 13.1ỵ Ratio and proportion Number 154 14ỵ Area and perimeter 14.1ỵ Area and perimeter Geometry and measure 164 Project 5: Picture frames 166 15ỵ Multiplying and dividing fractions and decimals 15.1ỵ Multiplying and dividing fractions 15.2ỵ Multiplying a decimal and a whole number Number 175 16ỵ Time 16.1ỵ Time intervals and time zones Geometry and measure 184 Project 6: Time for bed 185 17ỵ Number and the laws of arithmetic 17.1ỵ The laws of arithmetic Number 192 18ỵ Position and direction 18.1ỵ Coordinates and translation Geometry and measure 200 Glossary 208 Acknowledgements Addition and subtraction of fractions 9.1ỵ Addition and subtraction of fractions How to use this book How to use this book In this book you will find lots of different features to help your learning Questions to find out what you know already What you will learn in the unit Important words that you will use There are often many different ways to solve a problem Step-by-step examples showing a way to solve a problem These questions will help you develop your skills of thinking and working mathematically How to use this bookỵỵ An investigation to carry out with a partner or in groups Where this icon appears , the activity will help develop your skills of thinking and working mathematically Questions to help you think about how you learn This is what you have learned in the unit Questions that cover what you have learned in the unit At the end of several units, there is a project for you to carry out using what you have learned You might make something or solve a problem Projects and their accompanying teacher guidance have been written by the NRICH Team NRICH is an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge, which focuses on problem solving and on creating opportunities for students to learn mathematics through exploration and discussion: nrich.maths.org Thinking and Working Mathematically Thinking and Working Mathematically There are some important skills that you will develop as you learn mathematics Specialising is when I choose an example and check to see if it satisfies or does not satisfy specific mathematical criteria Characterising is when I identify and describe the mathematical properties of an object Generalising is when I recognise an underlying pattern by identifying many examples that satisfy the same mathematical criteria Classifying is when I organise objects into groups according to their mathematical properties Thinking and Working Mathematicallyỵỵ Critiquing is when I compare and evaluate mathematical ideas, representations or solutions to identify advantages and disadvantages Improving is when I refine mathematical ideas or representations to develop a more effective approach or solution Conjecturing is when I form mathematical questions or ideas Convincing is when I present evidence to justify or challenge a mathematical idea or solution These characteristics are reproduced from the Cambridge Primary Mathematics curriculum framework (0096) from 2020 This Cambridge International copyright material is reproduced under licence and remains the intellectual property of Cambridge Assessment International Education 1ỵ The number system Getting started 1ỵ Use digits to write these numbers aỵ Five thousand, two hundred and seventy-one bỵ One hundred and nine thousand and ninety 2ỵ What is the value of the digit in these numbers? aỵ 6703 bỵ 9060 cỵ 765430 3ỵ Copy and complete to decompose these numbers aỵ 805469 = + 5000 + bỵ 689567 = 600000 + + + +9 + 500 + + 4ỵ Zara scored 649 points in a computer game ỵ Which of the following is not a correct way to show her score? aỵ 600 + 40 + bỵ 600 + 49 cỵ 609 + dỵ 609 + 40 5ỵ Which of these numbers is 100 times larger than three hundred and thirty-three? aỵ 333 bỵ 3330 cỵ 33300 dỵ 333000 6ỵ Write the missing numbers 10 aỵ ữ 10 = 64 bỵ 509 ì cỵ ì 100 = 8000 dỵ 4400 ữ = 5090 = 44 The number systemỵỵỵỵ Place value is important because it helps you understand the meaning of a number You need place value to understand the order of numbers If someone offers you 30 dollars or 300 dollars, you need to know that 300 is more than 30 When you go shopping you will see lots of price labels What these labels have in common? €1.00 $1.49 ¥0.99 £2.99 In this unit you will learn more about decimal numbers Look at the examples in these pictures and talk with your partner about where you have seen decimal numbers 11 The number system 1.1 Understanding place value We are going to ãỵ explain the value of a digit in a decimal number (tenths and hundredths) ãỵ multiply and divide whole numbers by 1000 ãỵ multiply and divide decimals by 10 and 100 It is very important for a doctor to give the correct amount of medicine A dose of 10 ml is ten times greater than a dose of 1 ml and ten times smaller than a dose of 100ml composeỵ decimalỵ decimal place decimal pointỵ decomposeỵ hundredth place valueỵ tenth The value of a digit depends on its position in the number Think about what the digit is worth in these numbers Water $1.50 12 Water $1.50 Water $1.50 2.35 m 25 cents 1.1 Understanding place value Worked example Write this number in words and digits 10 000 + 2000 + 300 + 40 + + 0.6 + 0.07 Answer: Tip 12 345.67 Twelve thousand, three hundred and forty-five point six seven Use a place value grid to help you ỵ Remember to write the decimal part of the number as ‘six seven’ and not as ‘sixty-seven’ tenths hundredths ten thousands 10 000s 1000s 100s 10s 1s 1s 10 s 100 Exercise 1.1 1ỵ Write these numbers in digits aỵ One thousand and one point zero one bỵ Five hundred thousand and five point nine cỵ Four hundred and three thousand, and thirty-four point six six 2ỵ Write these numbers in words aỵ 345.09 bỵ 5378.12 cỵ 158ỵ 035.4 dỵ 3030.03 3ỵ What is the value of the digit in these numbers? aỵ 6703.46 bỵ 70213.8 cỵ 606456.7 dỵ 234560.07 13 The number system 4ỵ Write these numbers in words and digits aỵ 200000 + 6000 + 300 + + 0.1 bỵ 900000 + 90000 + 900 + + 0.9 cỵ 100 000 + 20 000 + 5000 + 600 + 20 + + 0.4 + 0.03 ỵ Swap books with your partner and check their answers 5ỵ Write the missing numbers aỵ 358 ì 100 = bỵ 2700 ữ = 27 cỵ 5600 ữ 1000 = dỵ 456 ì 1000 = 6ỵ Sofia multiplies a number by 10, then again by 10 and then again by 10 ỵ Her answer is 20000 ỵ What number did she start with? 7ỵ Write the missing numbers aỵ 3.45 ì 100 = bỵ 16.8 ữ 10 = cỵ 6.5 ì 10 = 8ỵ Find and correct the mistakes in this diagram 58.0 × 10 5800 ì 100 0.58 ữ 100 58 ữ 10 ì 1000 5.8 ỵ 5800 9ỵ Which missing number is the odd one out? Aỵ 33 ữ 10 = Cỵ ỵ 14 ì 10 = 30.3 Explain your answer Bỵ ì 100 = 330 Dỵ 3300 ữ 1000 = 1.2 Rounding decimal numbers Look back over your answers Did you use the worked example to help you? Did you find any question particularly hard? Why? Think like a mathematician Zara is thinking of a decimal number less than The hundredths digit is four more than the tenths digit The sum of the tenths digit and the hundredths digit is 10 What number is Zara thinking of? Make up a similar question to test your partner You will show you are specialising when you identify examples that fit the given criteria Look what I can do! ỵ I can explain the value of a digit in a decimal number (tenths and hundredths) ỵ I can multiply and divide whole numbers by 1000 ỵ I can multiply and divide decimals by 10 and 100 1.2 Rounding decimal numbers We are going to ãỵ round numbers with decimal place to the nearest whole number Rounding makes it easier to describe and understand numbers It is easier to understand ‘an African elephant is approximately metres tall’ than ‘the average height of an African elephant is 3.3 metres nearestỵ round round to the nearest 15 The number system Can you round these heights to the nearest whole number? Height of elephant 3.3 m Height of giraffe 5.5 m How tall are you? Height of ostrich 2.7 m Worked example Round these measurements to the nearest whole number bỵ 4.5mỵ aỵ 3.9mỵ cỵ 0.4m You can use a number line to help you Answer: aỵ 4m bỵ 5m cỵ 0m 16 If the tenths digit is 0, 1, 2, or 4, round down to the nearest whole number If the tenths digit is 5, 6, 7, or 9, round up to the nearest wholenumber 1.2 Rounding decimal numbers Exercise 1.2 1ỵ Identify the numbers marked by arrows Round each number to the nearest whole number A B C 2ỵ Round these numbers to the nearest whole number aỵ 65.8 bỵ 101.1 cỵ 44.4 dỵ 55.5 3ỵ Round these measures to the nearest whole centimetre aỵ 2.8cm bỵ 8.5cm Round these measures to the nearest whole metre cỵ 7.3m dỵ 0.3m 4ỵ A number with decimal place is rounded to the nearest whole number aỵ What is the smallest number that rounds to 5? bỵ What is the largest number that rounds to 5? ỵ Ask your partner to check your answers Did you both choose the same numbers? 5ỵ 74.5 is 74 to the nearest whole number ỵ Is Marcus correct? ỵ Explain your answer 6ỵ Use a calculator to help you answer this question ỵ Two numbers each with decimal place round to 231 to the nearest whole number ỵ The sum of the two numbers is 462 ỵ What could the numbers be? 17 The number system 7ỵ Use the clues to identify the correct number ỵ ỵ 10.42 9.73 9.9 9.37 7.83 10.1 8.7 9.55 The number: ãỵ has a tenths digit which is odd ãỵ rounds to 10 to the nearest whole number ãỵ has no hundredths digit ãỵ is less than 10 ỵ Swap books with your partner and check their answers Think about the questions you have just answered If you were asked similar questions, what would you differently? Think like a mathematician Roll a dice twice and make a number with decimal place Find all the different numbers you can make Round each of your numbers to the nearest whole number 2.5 rounds to 5.2 rounds to Roll the dice again and make some more numbers What numbers with decimal place are possible? Find all the possible numbers these could round to Look what I can do! ỵ I can round numbers with decimal place to the nearest whole number 18 1.2 Rounding decimal numbers Check your progress 1ỵ What is the value of the digit in these numbers? ỵ aỵ 6703.46 ỵ bỵ 7021.83 ỵ cỵ 606456.35 2ỵ Write these numbers in words and digits ỵ aỵ 100000 + 3000 + 500 + + 0.9 ỵ bỵ 600000 + 60000 + 600 + + 0.06 3ỵ aỵ What number is ten times bigger than 0.03? ỵ bỵ What number is one hundred times smaller than 555? 4ỵ Round these lengths to the nearest whole number ỵ aỵ 5.1m ỵ bỵ 16.5cm ỵ cỵ 10.4m ỵ dỵ 10.7cm 5ỵ Look at these number cards A 450 000 E ỵ B 45 45 000 F C 4.5 4500 G D 450 0.45 Write the letter of the card that is one hundredth of 45 6ỵ Write the missing numbers ỵ aỵ ữ 1000 = 20 ỵ bỵ 543 ì 1000 = ì 10 7ỵ What is the missing number? ỵ 100 ì 10 = 10000 ữ 8ỵ Sofia, Arun, Marcus and Zara each think of a number ỵ Their numbers are 3.5, 0.35, 35 and 0.53 ỵ Use these clues to find the number each is thinking of ỵ ãỵ Aruns number is ten times smaller than Marcuss number ỵ ãỵ Zaras number is not ten times smaller than Sofia’s or Arun’s or Marcus’s numbers ỵ ãỵ Sofias number is ten times smaller than Aruns number 19